You work for Leonard & Hofstadter, a financial intermediary. The company has written to various clients a

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Question:

You work for Leonard & Hofstadter, a financial intermediary. The company has written to various clients a total of 12,000 European 5-month call options and 7,000 European 8-month put options on Telstra stocks. The strike price of both the calls and puts is $3, while the stock is currently trading at $3.3 and offers a dividend yield of 0.5% p.a. Each option contract is on 1 share. You can assume a continuously compounded riskfree interest rate of 1.5% p.a. Based on the BSM model and the implied volatility of 25% p.a., you have calculated that the Delta, Gamma, Theta, Vega and Rho of each put option are -0.273, 0.493, -0.0004, 0.894 and -0.684 respectively.

NOTE:

For all answers show your calculations.

For underlying asset units and number of options contracts, round to the nearest integer.

In part a, round d1 and d2 to 2 decimal digits only when you need to compute the normal probabilities from the Normal Table. For all other calculations, including d1 and d2, round to 4 decimal digits at each step.

a) Relying on the same approach that you used for the puts, compute the Delta, Gamma, Theta, Vega and Rho of the company's overall option position. Next, you need to explain to your boss in plain English the meaning of each computed Greek letter.

b) Leonard & Hofstadter wants to make its portfolio Delta neutral. What trade needs to be made in order to do so?

c) Assume now the stock price increases to $3.4 instantly, what should the company do to maintain the Delta neutrality?

d) Assume now the stock price is still $3.3. The company is concerned with the risk of a changing riskfree interest rate and want to hedge its option portfolio against such risk, while keeping the portfolio delta neutral as well. To achieve this hedging objective, you are allowed to trade in 6-month call options on the same stock with strike of $2.8. The Delta, Gamma, Theta, Vega and Rho of these options are 0.850, 0.395, -0.0004, 0.537 and 1.122 respectively. Detail the trades that need to be made. Again, assume that each option is written on 1 share of Telstra stocks.